What is the nature of spacetime?

[tim9000]

I've been trying to learn about cosmological expansion (some weeks ago), I think I understand as much as any lay-person could, regarding why everything is moving away from our galaxy. However I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing, but something that has tangible, observable properties. Such as in observing closer galaxies lens more distant galaxies, or that the Alcubierre drive is theoretically possible...or moreover that a 'big rip' could tear the electrons from atomic nuclei, if expansion accelerates.
So if the space part of spacetime itself is getting bigger, and for the aforementioned reasons space is presumably more than just a vacuum of quantum mechanical fluctuations (with various standard model fields in it). Then does humanity actually know what spacetime is, or is it still more or less a mystery?

Thank youP.S. I forgot, of course gravitational waves.

 

[phinds]

Spacetime is a framework in which things happen. It is geometry. It is NOT a "fabric" or other pop-science nonsense. Expansion is just things getting farther apart, not space "stretching" or "expanding". The "big rip" is not in the cards based on our current understanding of cosmology and even if it were that would not make spacetime anything other than a framework. Light does not get "bent" when it passes a massive object, it follows a straight line, BUT ... that "straight line" is in Riemann Geometry (which describes spacetime) not Euclidean Geometry which is why it is described as "bent" from a human point of view.

 

[FactChecker]

There is a trade-off between a person going through time and the same person going through space (at a fast speed). To understand that, time and space need to be put into the same coordinate system. It is similar to the trade-off that a person traveling at a constant speed in two physical dimensions. Suppose a person is traveling at a constant 50 miles per hour. If he goes North at 50 mph, then you know he is not going East or West at all. Likewise if he is going East at 50 mph, you know he is not going North or South at all. In space-time we are always going at the speed of light. If we go at the speed of light in physical space, then you know that we are not moving in time at all. Likewise, if we go full speed in time, then you know we are not moving in physical space at all.

Far from metaphysical, the distortion of space-time is very real. It explains gravity. Einstein's General Relativity is all about that. That is about as "down-to-Earth" as you can get. (Pun intended.)

 

[Dale]

I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing

In science a thing is identified with its measurable properties. So an electron is a thing with a certain combination of measurable properties including mass, spin, and charge.

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

 

[bhobba]

However I still don't understand what spacetime is.

Due to the symmetry properties of space and time as measured using rulers, clocks or whatever, its turns out its like space by itself - it can in a sense be 'rotated' so you can't consider them separate. If you have a stick and you can't get it through a door you can rotate it to get it through. The same with space and time.

Here is the technical detail:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Length contraction, time dilation etc is just like rotating a rod to go through a door - except its 'hyperbolic' rotation.

Thanks
Bill

 

[tim9000]

Spacetime is a framework in which things happen. It is geometry. It is NOT a "fabric" or other pop-science nonsense. Expansion is just things getting farther apart, not space "stretching" or "expanding". The "big rip" is not in the cards based on our current understanding of cosmology and even if it were that would not make spacetime anything other than a framework. Light does not get "bent" when it passes a massive object, it follows a straight line, BUT ... that "straight line" is in Riemann Geometry (which describes spacetime) not Euclidean Geometry which is why it is described as "bent" from a human point of view.

H'mm, yeah I see how light can bend around a galaxy, yet still be traveling 'straight', due to spacetime being a curvature of the geometry itself.
However, (and I don't mean to irritate, but) it is the other implications of proper distances getting bigger (over "time"?) or possibly in a big rip scenario tearing electrons from nucleus. I understand how that sentence is true, just not like how can this 'geometry' becomes this fabric of creation that is tangible with real consequences. And is presumably has properties as I address in my response to Dale below.

There is a trade-off between a person going through time and the same person going through space (at a fast speed). To understand that, time and space need to be put into the same coordinate system. It is similar to the trade-off that a person traveling at a constant speed in two physical dimensions. Suppose a person is traveling at a constant 50 miles per hour. If he goes North at 50 mph, then you know he is not going East or West at all. Likewise if he is going East at 50 mph, you know he is not going North or South at all. In space-time we are always going at the speed of light. If we go at the speed of light in physical space, then you know that we are not moving in time at all. Likewise, if we go full speed in time, then you know we are not moving in physical space at all.

Far from metaphysical, the distortion of space-time is very real. It explains gravity. Einstein's General Relativity is all about that. That is about as "down-to-Earth" as you can get. (Pun intended.)

That is actually a really good way of putting it, nice sort of vector-ie way of putting it.

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

I sort of understand that, how would you define it? I understand that is has these quantum fluctuations (creation and destruction of particles spontaneously, really fast) as well as these fields through it (Higgs, electromagnetic...and others? Sorry, what are they?)
I'm trying to get my head around the QED and QCD vacuum wiki pages.
Presumably these quantum fields in the standard model are are of this spacetime geometry, I.e. when the light travels around a galaxy, the electromagnetic field is distorted by the mass of the galaxy it passes around so that 'straight' from the perspective of the light or the EM field is around the galaxy?Thanks all!

 

[Dale]

I understand that is has these quantum fluctuations (creation and destruction of particles spontaneously, really fast) as well as these fields through it (Higgs, electromagnetic...and others? Sorry, what are they?)
I'm trying to get my head around the QED and QCD vacuum wiki pages.
Presumably these quantum fields in the standard model are are of this spacetime geometry, I.e. when the light travels around a galaxy, the electromagnetic field is distorted by the mass of the galaxy it passes around so that 'straight' from the perspective of the light or the EM field is around the galaxy?

GR is a classical (non quantum) theory. None of this is going to help you understand GR.

 

[pervect]

I've been trying to learn about cosmological expansion (some weeks ago), I think I understand as much as any lay-person could, regarding why everything is moving away from our galaxy. However I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing, but something that has tangible, observable properties. Such as in observing closer galaxies lens more distant galaxies, or that the Alcubierre drive is theoretically possible...or moreover that a 'big rip' could tear the electrons from atomic nuclei, if expansion accelerates.
So if the space part of spacetime itself is getting bigger, and for the aforementioned reasons space is presumably more than just a vacuum of quantum mechanical fluctuations (with various standard model fields in it). Then does humanity actually know what spacetime is, or is it still more or less a mystery?

Thank youP.S. I forgot, of course gravitational waves.

I would say that the fundamental observable phenomenon of space-time is the ability to measure distances, and time intervals. You can pretty much regard this as being done with rulers, and clocks. If you wax philosophical, you can probably agonize a lot over what a ruler and a clock really is. As far as science goes, we have an operational procedure based on the SI standard for measuring both.

I can dig up a quote for the "SI meter" and the "SI second" definition if one is needed, but it should be easy to find.

Space time is geometry, and we can regard geometry as the study of distances. Angles a a part of geometry, but if we have distances, we can compasses drawing circles, and we can imagine measuring distances along the arcs of these circles, and those define angles, so we can define angles in terms of distances. Thus we don't need to regard geometry as being about angles and distances, since we can define angles in terms of distance. We can regard geometry as being fundamentally about distances.

It's helpful to introduce the concept of coordinates to talk about geometry, though not strictly necessary. Since it's not strictly necessary, I will avoid it for now.

Space-time geometry takes a rather funny turn, in that there turns out not to be two separate sorts of distances (spatial distances and time distances, usually referred to as time intervals), but only one sort of "distance", an observer independent interval known at the Lorentz interval. The relationship between the Lorentz interval and the SI concepts of time interval and distance is one of the topics of special relativity, and the reason that we view space-time as a single unified entity rather than two separate concepts of space and time.

But you can compute the space-time interval knowing only how to measure distances and time intervals. So if you understand distances and time intervals, you have the tools needed to understand the Lorentz interval.

There are some tricky aspects about distance that I've glossed over, but the main point I'm trying to make is that you can regard space-time as being all about distances, and that we have operational procedures for measuring distance via instruments we call rulers and clocks.

 

[FactChecker]

That is actually a really good way of putting it, nice sort of vector-ie way of putting it.

If you like that way of explaining relativity, I highly recommend the book "Relativity Visualized" by Lewis Epstein. I got that idea from his book. I really enjoyed reading it.

 

[PeterDonis]

or that the Alcubierre drive is theoretically possible

"Theoretically possible" in the sense that it is a valid mathematical solution of the Einstein Field Equation, yes. But it is a solution that in all probability does not describe an actual physically possible state of affairs. The examples of gravitational lensing and gravitational waves are better since we know they actually happen.

 

[Narasoma]

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself. While metric is just a mathematical property of a spacetime model, i.e. differentiable manifold. By the way, is it possible to make a model of the spacetime using some mathematical objects other than a differentiable manifold, or, more generally a topological space?

 

[jbriggs444]

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself.

What difference does it make?

 

[FactChecker]

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself. While metric is just a mathematical property of a spacetime model, i.e. differentiable manifold. By the way, is it possible to make a model of the spacetime using some mathematical objects other than a differentiable manifold, or, more generally a topological space?

"spacetime" is the idea that explains the time and distance measurements that we observe in the universe and in physics experiments. If we ignore measurements, what is left to be called "knowledge"?

 

[Narasoma]

What difference does it make?

Of course, something which is "there" is different from something which is the result of our conception. However, whether that difference has a significant physical effect or not, I don't know.

 

[Dale]

How do we know that spacetime is "there" and not just an "illusion" made by our brain?

I am with jbriggs444 on this. This question and its answer don't matter. Whether it is all in our head or not we have a theory which accurately predicts the outcome of measurements involving clocks and rulers.

 

[Narasoma]

"spacetime" is the idea that explains the time and distance measurements that we observe in the universe and in physics experiments. If we ignore measurements, what is left to be called "knowledge"?

Is there any way to formulate a measurement other than using metric?
(But this is just a restriction to my earlier question)

 

[Narasoma]

I am with jbriggs444 on this. This question and its answer don't matter. Whether it is all in our head or not we have a theory which accurately predicts the outcome of measurements involving clocks and rulers.

Maybe it's just a matter of philosophy. But to me it's still bothering.

 

[FactChecker]

Is there any way to formulate a measurement other than using metric?
(But this is just a restriction to my earlier question)

It's important to understand that the distortions of space and time measurements apply to ANY method of measurement: the aging of a human, the vibrations of atoms, the time for Mercury to orbit the Sun. It means that we can take an atomic clock to the top of a mountain and it will have run faster when we bring it down and compare it with a lower-altitude clock. The distortion also explains gravity. That is in Einstein's general theory. So it is not just an intellectual mind-game.

 

[Narasoma]

It's important to understand that the distortions of space and time measurements apply to ANY method of measurement: the aging of a human, the vibrations of atoms, the time for Mercury to orbit the Sun. It means that we can take an atomic clock to the top of a mountain and it will have run faster when we bring it down and compare it with a lower-altitude clock. The distortion also explains gravity. That is in Einstein's general theory. So it is not just an intellectual mind-game.

Hm, this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds. In our solar system scale, GR gave a very accurate prediction. However, there still some mysteries out there, dark matter and dark energy for example. We say that there is a dark matter and dark energy is because we keep GR the way it is, or in other words, we keep a differentiable manifold as our model of the spacetime.

 

[phinds]

Hm, this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds. In our solar system scale, GR gave a very accurate prediction. However, there still some mysteries out there, dark matter and dark energy for example. We say that there is a dark matter and dark energy is because we keep GR the way it is, or in other words, we keep a differentiable manifold as our model of the spacetime.

I don't think dark matter has anything to do with GR. Am I missing something?

 

[Ibix]

I don't think dark matter has anything to do with GR. Am I missing something?

I think one has to posit something like dark matter to make GR consistent with the observed rotational profile of galaxies. However, to address what I suspect is narasoma's point, that doesn't mean that we didn't consider modifying GR rather than proposing a new kind of matter. It's just that the modified gravity theories haven't panned out and there is increasing indirect evidence for a kind of matter we haven't seen directly yet.

 

[phinds]

I think one has to posit something like dark matter to make GR consistent with the observed rotational profile of galaxies.

But wouldn't the same be true for Newtonian mechanics? In fact, wasn't it an application of Newtonian mechanics to the rotational speed that led to the realization of dark matter? My point being that dark matter per se isn't needed for GR it's just that there is something (that we call dark matter) that affects the rotational speeds and the flatness or near-flatness of the universe. I may just be tying myself in a knot w/ definitions here.

 

[Ibix]

But wouldn't the same be true for Newtonian mechanics? In fact, wasn't it an application of Newtonian mechanics to the rotational speed that led to the realization of dark matter? My point being that dark matter per se isn't needed for GR it's just that there is something (that we call dark matter) that affects the rotational speeds and the flatness or near-flatness of the universe. I may just be tying myself in a knot w/ definitions here.

I see what you're getting at. I think we're talking slightly at cross purposes. I agree that you don't need dark matter to make GR work, but you do need some invisible source of gravity to make it describe galaxies correctly. I was interpreting the question as "why do we add dark matter instead of thinking of revising GR", the answer to which is that we did try revising gravity (Newtonian gravity - you are right) but couldn't make it work, especially in light of more recent observations. Subject to the usual "all science is our current best guess" caveats, of course.

 

[Narasoma]

I don't think dark matter has anything to do with GR. Am I missing something?

Fact : We "saw" ordinary matter acted strangely
Conclusion : We said that there is "something" caused that strangeness.

But this conclusion has been taken because of keeping GR in mind. My question is if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold, maybe we didn't see dark matter or dark energy again. But this is just my brute force imagination.

 

[PeterDonis]

if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold

Can you give specific examples of theories along these lines that are being investigated? We can't discuss personal speculations.

 

[Ibix]

But this conclusion has been taken because of keeping GR in mind. My question is if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold, maybe we didn't see dark matter or dark energy again. But this is just my brute force imagination.

That's kind of the point I was making. We have considered alternatives (e.g. MOND: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics), and the wiki article links to papers as recent as 2012 on the subject. But my understanding is that unmodified GR plus dark matter is generally considered to be the better hypothesis given our current state of knowledge.

 

[Dale]

this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds

If that was your question then you should have worded it this way, not is it "an 'illusion' made by our brain". That overly provocative wording completely obscured this intention.

I am almost certain that we can make a different mathematical model. Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

However, those would just be considered different formulations of the same theory, not a new theory. It would still be GR unless it led to different predictions.

 

[PeterDonis]

We have considered alternatives

MOND still models spacetime as a differentiable manifold. Narasoma is talking about not using a manifold structure at all.

 

[PeterDonis]

Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

Both of those use differentiable manifolds to model spacetime. That's a big part of why they can be shown to be mathematically equivalent. Showing mathematical equivalency between a model that uses a differentiable manifold and a model that doesn't is a much taller order.

 

[Narasoma]

If that was your question then you should have worded it this way, not is it "an 'illusion' made by our brain". That overly provocative wording completely obscured this intention.

I am almost certain that we can make a different mathematical model. Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

However, those would just be considered different formulations of the same theory, not a new theory. It would still be GR unless it led to different predictions.

So, you mean that if we want to build a new theory, it is not enough just by changing of our "modelisation"?
I haven't considered that.